arXiv subjects

Naoto Ohsaka

Publications and source records attributed to Naoto Ohsaka.

At least 19 recordsLinked to original sources

arXiv2026

Tight Inapproximability of Target Set Reconfiguration

Given a graph $G$ with a vertex threshold function $τ$, consider a dynamic process in which any inactive vertex $v$ becomes activated whenever at least $τ(v)$ of its neighbors have been activated. A vertex set $S$ is called a target set if all vertices of $G$ would eventually be activated when initially activating exactly the vertices of $S$. In the Minmax Target Set Reconfiguration problem, for a graph $G$ and a pair of its target sets $X$ and $Y$, we wish to transform $X$ into $Y$ by repeatedly adding or removing a single vertex, using only target sets of $G$, so as to minimize the maximum size of any intermediate target set. We prove that it is $\mathbf{NP}$-hard to approximate Minmax Target Set Reconfiguration within a factor of $2-o\left(\frac{1}{\operatorname{polylog} n}\right)$, where $n$ is the number of vertices. Our result establishes a tight lower bound on approximability of Minmax Target Set Reconfiguration, which admits a simple $2$-factor approximation algorithm. The proof is based on a gap-preserving reduction from Target Set Selection to Minmax Target Set Reconfiguration, where $\mathbf{NP}$-hardness of approximation for the former problem is proven by Chen (SIDMA 2009) and Charikar, Naamad, and Wirth (APPROX/RANDOM 2016).

cs.DS↗

arXiv2026

Optimal PSPACE-hardness of Approximating $q$-CSP Reconfiguration

In the Maxmin $q$-CSP Reconfiguration problem, given a satisfiable $q$-CSP instance and a pair of its satisfying assignments, we are asked to transform one assignment into the other by repeatedly changing the value assigned to a single variable. The objective is to find such a transformation that maximizes the minimum fraction of satisfied constraints along the transformation. In this paper, we prove that for any $q \geq 2$ and $\varepsilon > 0$, Maxmin $q$-CSP Reconfiguration is $\mathsf{PSPACE}$-hard to approximate within a factor of $\frac{1}{2^{q-1}}+\varepsilon$. To complement this hardness result, we prove that a $\bigl(\frac{1}{2^{q-1}}-\varepsilon\bigr)$-factor approximation for Maxmin $q$-CSP Reconfiguration is in $\mathsf{NP}$ in the perfect completeness case. These results establish the optimal $\mathsf{PSPACE}$-hardness of approximating Maxmin $q$-CSP Reconfiguration for every $q \geq 2$ under $\mathsf{NP} \neq \mathsf{PSPACE}$.

cs.CC↗

arXiv2026

On (In)approximability of MaxMin Independent Set Reconfiguration

In the Independent Set Reconfiguration problem under the Token Addition/Removal rule, given a graph $G$ and two independent sets $I$ and $J$ of $G$, we want to transform $I$ into $J$ by adding and removing vertices, such that all the sets throughout the process are independent sets. Its approximate version called MaxMin Independent Set Reconfiguration aims to maximise the minimum size of the independent sets in the process above. We study the (in)approximability of this problem for general graphs as well as restricted graph classes. Firstly, on general graphs, we obtain a polynomial-time $(n / \log n)$-factor approximation algorithm, complementing the $\mathsf{PSPACE}$-hardness of $n^{Ω(1)}$-factor approximation due to Hirahara and Ohsaka [STOC 2024, ICALP 2024] and the $\mathsf{NP}$-hardness of $n^{1-\varepsilon}$-factor approximation due to Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno [TCS 2011]. Secondly, we present a polynomial-time approximation algorithm for degenerate graphs as well as $\mathsf{FPT}$-approximation schemes for bounded-treewidth graphs and $H$-minor-free graphs. Lastly, we extend the above inapproximability results to bounded-degree graphs, graphs of bandwidth $n^{\frac{1}{2}+Θ(1)}$, and bipartite graphs.

cs.DS↗

arXiv2026

DiverXplorer: Stock Image Exploration via Diversity Adjustment for Graphic Design

Graphic designers explore large stock image collections during open-ended or early-stage design tasks, yet common tools emphasize relevance and similarity, limiting designers' ability to overview the design space or discover visual patterns. We present an image exploration prototype that enables stepwise adjustment of diversity, allowing users to transition from diverse overviews to increasingly focused subsets during exploration. Our approach implements diversity control via determinantal point process (DPP)-based sampling and exposes diversity-similarity tradeoffs through interaction rather than static ranking. We report findings from a pilot study with professional graphic designers comparing our technique to baselines inspired by current tools in open-ended image selection tasks. Results suggest that stepwise diversity control supports early-stage sensemaking and comparison of visual patterns, while revealing important tradeoffs: diversity aids discovery and reduces backtracking, but becomes less desirable as exploration progresses. We aim to provide a novel perspective on how to implement transitions between diversity and similarity. Our code is available at https://github.com/CyberAgentAILab/DiverXplorer.

cs.HC↗

arXiv2025

Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules

In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier work focused on modifying a single element at a time, recent studies have started examining how different rules impact computational complexity. Motivated by recent progress, we study Independent Set Reconfiguration (ISR) and Vertex Cover Reconfiguration (VCR) under the $k$-Token Jumping ($k$-TJ) and $k$-Token Sliding ($k$-TS) models. In $k$-TJ, up to $k$ vertices may be replaced, while $k$-TS additionally requires a perfect matching between removed and added vertices. It is known that the complexity of ISR crucially depends on $k$, ranging from PSPACE-complete and NP-complete to polynomial-time solvable. In this paper, we further explore the gradient of computational complexity of the problems. We first show that ISR under $k$-TJ with $k = |I| - μ$ remains NP-hard when $μ$ is any fixed positive integer and the input graph is restricted to graphs of maximum degree 3 or planar graphs of maximum degree 4, where $|I|$ is the size of feasible solutions. In addition, we prove that the problem belongs to NP not only for $μ=O(1)$ but also for $μ= O(\log |I|)$. In contrast, we show that VCR under $k$-TJ is in XP when parameterized by $μ= |S| - k$, where $|S|$ is the size of feasible solutions. Furthermore, we establish the PSPACE-completeness of ISR and VCR under both $k$-TJ and $k$-TS on several graph classes, for fixed $k$ as well as superconstant $k$ relative to the size of feasible solutions.

cs.CC↗

arXiv2025

Asymptotically Optimal Inapproximability of E$k$-SAT Reconfiguration

In the Maxmin E$k$-SAT Reconfiguration problem, we are given a satisfiable $k$-CNF formula $φ$ where each clause contains exactly $k$ literals, along with a pair of its satisfying assignments. The objective is transform one satisfying assignment into the other by repeatedly flipping the value of a single variable, while maximizing the minimum fraction of satisfied clauses of $φ$ throughout the transformation. In this paper, we demonstrate that the optimal approximation factor for Maxmin E$k$-SAT Reconfiguration is $1 - Θ\left(\frac{1}{k}\right)$. On the algorithmic side, we develop a deterministic $\left(1-\frac{1}{k-1}-\frac{1}{k}\right)$-factor approximation algorithm for every $k \geq 3$. On the hardness side, we show that it is $\mathsf{PSPACE}$-hard to approximate this problem within a factor of $1-\frac{1}{10k}$ for every sufficiently large $k$. Note that an ``$\mathsf{NP}$ analogue'' of Maxmin E$k$-SAT Reconfiguration is Max E$k$-SAT, whose approximation threshold is $1-\frac{1}{2^k}$ shown by Håstad (JACM 2001). To the best of our knowledge, this is the first reconfiguration problem whose approximation threshold is (asymptotically) worse than that of its $\mathsf{NP}$ analogue. To prove the hardness result, we introduce a new ``non-monotone'' test, which is specially tailored to reconfiguration problems, despite not being helpful in the PCP regime.

cs.CC↗

arXiv2025

Asymptotically Optimal Inapproximability of Maxmin $k$-Cut Reconfiguration

$k$-Coloring Reconfiguration is one of the most well-studied reconfiguration problems, which asks to transform a given proper $k$-coloring of a graph to another by repeatedly recoloring a single vertex. Its approximate version, Maxmin $k$-Cut Reconfiguration, is defined as an optimization problem of maximizing the minimum fraction of bichromatic edges during the transformation between (not necessarily proper) $k$-colorings. In this paper, we prove that the optimal approximation factor of this problem is $1 - Θ\left(\frac{1}{k}\right)$ for every $k \ge 2$. Specifically, we show the $\mathsf{PSPACE}$-hardness of approximating the objective value within a factor of $1 - \frac{\varepsilon}{k}$ for some universal constant $\varepsilon > 0$, whereas we present a deterministic polynomial-time algorithm that achieves the approximation factor of $1 - \frac{2}{k}$. To prove the hardness result, we develop a new probabilistic verifier that tests a ``striped'' pattern. Our polynomial-time algorithm is based on ``a random reconfiguration via a random solution,'' i.e., the transformation that goes through one random $k$-coloring.

cs.CC↗

arXiv2025

On Approximate Reconfigurability of Label Cover

Given a two-prover game $G$ and its two satisfying labelings $ψ_\mathsf{ini}$ and $ψ_\mathsf{tar}$, the Label Cover Reconfiguration problem asks whether $ψ_\mathsf{ini}$ can be transformed into $ψ_\mathsf{tar}$ by repeatedly changing the label of a single vertex while preserving any intermediate labeling satisfying $G$. We consider its optimization version by relaxing the feasibility of labelings, referred to as Maxmin Label Cover Reconfiguration: We are allowed to pass through any non-satisfying labelings, but required to maximize the ``soundness error,'' which is defined as the minimum fraction of satisfied edges during transformation from $ψ_\mathsf{ini}$ to $ψ_\mathsf{tar}$. Since the parallel repetition theorem of Raz (SIAM J. Comput., 1998), which implies $\mathbf{NP}$-hardness of approximating Label Cover within any constant factor, gives strong inapproximability results for many $\mathbf{NP}$-hard problems, one may think of using Maxmin Label Cover Reconfiguration to derive inapproximability results for reconfiguration problems. We prove the following results on Maxmin Label Cover Reconfiguration, which display different trends from those of Label Cover and the parallel repetition theorem: $\bullet$ Maxmin Label Cover Reconfiguration can be approximated within a factor of $\frac{1}{4} - o(1)$ for some restricted graph classes, including biregular graphs, balanced bipartite graphs with no isolated vertices, and superconstant average degree graphs. $\bullet$ A ``naive'' parallel repetition of Maxmin Label Cover Reconfiguration does not decrease the soundness error for every two-prover game. $\bullet$ Label Cover Reconfiguration on projection games can be decided in polynomial time. Our results suggest that a reconfiguration analogue of the parallel repetition theorem is unlikely.

cs.DM↗

arXiv2024

Matroid Semi-Bandits in Sublinear Time

We study the matroid semi-bandits problem, where at each round the learner plays a subset of $K$ arms from a feasible set, and the goal is to maximize the expected cumulative linear rewards. Existing algorithms have per-round time complexity at least $Ω(K)$, which becomes expensive when $K$ is large. To address this computational issue, we propose FasterCUCB whose sampling rule takes time sublinear in $K$ for common classes of matroids: $O(D\text{ polylog}(K)\text{ polylog}(T))$ for uniform matroids, partition matroids, and graphical matroids, and $O(D\sqrt{K}\text{ polylog}(T))$ for transversal matroids. Here, $D$ is the maximum number of elements in any feasible subset of arms, and $T$ is the horizon. Our technique is based on dynamic maintenance of an approximate maximum-weight basis over inner-product weights. Although the introduction of an approximate maximum-weight basis presents a challenge in regret analysis, we can still guarantee an upper bound on regret as tight as CUCB in the sense that it matches the gap-dependent lower bound by Kveton et al. (2014a) asymptotically.

cs.LG↗

arXiv2024

Gap Amplification for Reconfiguration Problems

In this paper, we demonstrate gap amplification for reconfiguration problems. In particular, we prove an explicit factor of PSPACE-hardness of approximation for three popular reconfiguration problems only assuming the Reconfiguration Inapproximability Hypothesis (RIH) due to Ohsaka (STACS 2023). Our main result is that under RIH, Maxmin 2-CSP Reconfiguration is PSPACE-hard to approximate within a factor of $0.9942$. Moreover, the same result holds even if the constraint graph is restricted to $(d,λ)$-expander for arbitrarily small $\fracλ{d}$. The crux of its proof is an alteration of the gap amplification technique due to Dinur (J. ACM, 2007), which amplifies the $1$ vs. $1-\varepsilon$ gap for arbitrarily small $\varepsilon \in (0,1)$ up to the $1$ vs. $1-0.0058$ gap. As an application of the main result, we demonstrate that Minmax Set Cover Reconfiguration and Minmax Dominating Set Reconfiguratio} are PSPACE-hard to approximate within a factor of $1.0029$ under RIH. Our proof is based on a gap-preserving reduction from Label Cover to Set Cover due to Lund and Yannakakis (J. ACM, 1994). Unlike Lund--Yannakakis' reduction, the expander mixing lemma is essential to use. We highlight that all results hold unconditionally as long as "PSPACE-hard" is replaced by "NP-hard," and are the first explicit inapproximability results for reconfiguration problems without resorting to the parallel repetition theorem. We finally complement the main result by showing that it is NP-hard to approximate Maxmin 2-CSP Reconfiguration within a factor better than $\frac{3}{4}$.

cs.DM↗

arXiv2024

Safe Collaborative Filtering

Excellent tail performance is crucial for modern machine learning tasks, such as algorithmic fairness, class imbalance, and risk-sensitive decision making, as it ensures the effective handling of challenging samples within a dataset. Tail performance is also a vital determinant of success for personalized recommender systems to reduce the risk of losing users with low satisfaction. This study introduces a "safe" collaborative filtering method that prioritizes recommendation quality for less-satisfied users rather than focusing on the average performance. Our approach minimizes the conditional value at risk (CVaR), which represents the average risk over the tails of users' loss. To overcome computational challenges for web-scale recommender systems, we develop a robust yet practical algorithm that extends the most scalable method, implicit alternating least squares (iALS). Empirical evaluation on real-world datasets demonstrates the excellent tail performance of our approach while maintaining competitive computational efficiency.

cs.IR↗

arXiv2024

Optimal PSPACE-hardness of Approximating Set Cover Reconfiguration

In the Minmax Set Cover Reconfiguration problem, given a set system $\mathcal{F}$ over a universe and its two covers $\mathcal{C}^\mathsf{start}$ and $\mathcal{C}^\mathsf{goal}$ of size $k$, we wish to transform $\mathcal{C}^\mathsf{start}$ into $\mathcal{C}^\mathsf{goal}$ by repeatedly adding or removing a single set of $\mathcal{F}$ while covering the universe in any intermediate state. Then, the objective is to minimize the maximize size of any intermediate cover during transformation. We prove that Minmax Set Cover Reconfiguration and Minmax Dominating Set Reconfiguration are $\mathsf{PSPACE}$-hard to approximate within a factor of $2-\frac{1}{\operatorname{polyloglog} N}$, where $N$ is the size of the universe and the number of vertices in a graph, respectively, improving upon Ohsaka (SODA 2024) and Karthik C. S. and Manurangsi (2023). This is the first result that exhibits a sharp threshold for the approximation factor of any reconfiguration problem because both problems admit a $2$-factor approximation algorithm as per Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno (Theor. Comput. Sci., 2011). Our proof is based on a reconfiguration analogue of the FGLSS reduction from Probabilistically Checkable Reconfiguration Proofs of Hirahara and Ohsaka (2024). We also prove that for any constant $\varepsilon \in (0,1)$, Minmax Hypergraph Vertex Cover Reconfiguration on $\operatorname{poly}(\varepsilon^{-1})$-uniform hypergraphs is $\mathsf{PSPACE}$-hard to approximate within a factor of $2-\varepsilon$.

cs.CC↗

arXiv2024

On the Parameterized Intractability of Determinant Maximization

In the Determinant Maximization problem, given an $n\times n$ positive semi-definite matrix $\bf{A}$ in $\mathbb{Q}^{n\times n}$ and an integer $k$, we are required to find a $k\times k$ principal submatrix of $\bf{A}$ having the maximum determinant. This problem is known to be NP-hard and further proven to be W[1]-hard with respect to $k$ by Koutis. However, there is still room to explore its parameterized complexity in the restricted case, in the hope of overcoming the general-case parameterized intractability. In this study, we rule out the fixed-parameter tractability of Determinant Maximization even if an input matrix is extremely sparse or low rank, or an approximate solution is acceptable. We first prove that Determinant Maximization is NP-hard and W[1]-hard even if an input matrix is an arrowhead matrix; i.e., the underlying graph formed by nonzero entries is a star, implying that the structural sparsity is not helpful. By contrast, Determinant Maximization is known to be solvable in polynomial time on tridiagonal matrices. Thereafter, we demonstrate the W[1]-hardness with respect to the rank $r$ of an input matrix. Our result is stronger than Koutis' result in the sense that any $k\times k$ principal submatrix is singular whenever $k>r$. We finally give evidence that it is W[1]-hard to approximate Determinant Maximization parameterized by $k$ within a factor of $2^{-c\sqrt{k}}$ for some universal constant $c>0$. Our hardness result is conditional on the Parameterized Inapproximability Hypothesis posed by Lokshtanov, Ramanujan, Saurab, and Zehavi, which asserts that a gap version of Binary Constraint Satisfaction Problem is W[1]-hard. To complement this result, we develop an $\varepsilon$-additive approximation algorithm that runs in $\varepsilon^{-r^2}\cdot r^{O(r^3)}\cdot n^{O(1)}$ time for the rank $r$ of an input matrix, provided that the diagonal entries are bounded.

cs.DS↗

arXiv2024

Alphabet Reduction for Reconfiguration Problems

We present a reconfiguration analogue of alphabet reduction à la Dinur (J. ACM, 2007) and its applications. Given a binary constraint graph $G$ and its two satisfying assignments $ψ^\mathsf{ini}$ and $ψ^\mathsf{tar}$, the Maxmin Binary CSP Reconfiguration problem requests to transform $ψ^\mathsf{ini}$ into $ψ^\mathsf{tar}$ by repeatedly changing the value of a single vertex so that the minimum fraction of satisfied edges is maximized. We demonstrate a polynomial-time reduction from Maxmin Binary CSP Reconfiguration with arbitrarily large alphabet size $W \in \mathbb{N}$ to itself with universal alphabet size $W_0 \in \mathbb{N}$ such that 1. the perfect completeness is preserved, and 2. if any reconfiguration for the former violates $\varepsilon$-fraction of edges, then $Ω(\varepsilon)$-fraction of edges must be unsatisfied during any reconfiguration for the latter. The crux of its construction is the reconfigurability of Hadamard codes, which enables to reconfigure between a pair of codewords, while avoiding getting too close to the other codewords. Combining this alphabet reduction with gap amplification due to Ohsaka (SODA 2024), we are able to amplify the $1$ vs. $1-\varepsilon$ gap for arbitrarily small $\varepsilon \in (0,1)$ up to the $1$ vs. $1-\varepsilon_0$ for some universal $\varepsilon_0 \in (0,1)$ without blowing up the alphabet size. In particular, a $1$ vs. $1-\varepsilon_0$ gap version of Maxmin Binary CSP Reconfiguration with alphabet size $W_0$ is PSPACE-hard only assuming the Reconfiguration Inapproximability Hypothesis posed by Ohsaka (STACS 2023), whose gap parameter can be arbitrarily small. This may not be achieved only by gap amplification of Ohsaka, which makes the alphabet size gigantic depending on the gap value of the hypothesis.

cs.CC↗

arXiv2023

Probabilistically Checkable Reconfiguration Proofs and Inapproximability of Reconfiguration Problems

Motivated by the inapproximability of reconfiguration problems, we present a new PCP-type characterization of PSPACE, which we call a probabilistically checkable reconfiguration proof (PCRP): Any PSPACE computation can be encoded into an exponentially long sequence of polynomially long proofs such that every adjacent pair of the proofs differs in at most one bit, and every proof can be probabilistically checked by reading a constant number of bits. Using the new characterization, we prove PSPACE-completeness of approximate versions of many reconfiguration problems, such as the Maxmin $3$-SAT Reconfiguration problem. This resolves the open problem posed by Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno (ISAAC 2008; Theor. Comput. Sci. 2011) as well as the Reconfiguration Inapproximability Hypothesis by Ohsaka (STACS 2023) affirmatively. We also present PSPACE-completeness of approximating the Maxmin Clique Reconfiguration problem to within a factor of $n^ε$ for some constant $ε> 0$.

cs.CC↗

arXiv2023

Fast and Examination-agnostic Reciprocal Recommendation in Matching Markets

In matching markets such as job posting and online dating platforms, the recommender system plays a critical role in the success of the platform. Unlike standard recommender systems that suggest items to users, reciprocal recommender systems (RRSs) that suggest other users must take into account the mutual interests of users. In addition, ensuring that recommendation opportunities do not disproportionately favor popular users is essential for the total number of matches and for fairness among users. Existing recommendation methods in matching markets, however, face computational challenges on real-world scale platforms and depend on specific examination functions in the position-based model (PBM). In this paper, we introduce the reciprocal recommendation method based on the matching with transferable utility (TU matching) model in the context of ranking recommendations in matching markets, and propose a faster and examination-agnostic algorithm. Furthermore, we evaluate our approach on experiments with synthetic data and real-world data from an online dating platform in Japan. Our method performs better than or as well as existing methods in terms of the total number of matches and works well even in relatively large datasets for which one existing method does not work.

cs.IR↗

arXiv2023

Gap Preserving Reductions Between Reconfiguration Problems

Combinatorial reconfiguration is a growing research field studying problems on the transformability between a pair of solutions of a search problem. We consider the approximability of optimization variants of reconfiguration problems; e.g., for a Boolean formula $φ$ and two satisfying truth assignments $σ_{\sf s}$ and $σ_{\sf t}$ for $φ$, Maxmin SAT Reconfiguration requires to maximize the minimum fraction of satisfied clauses of $φ$ during transformation from $σ_{\sf s}$ to $σ_{\sf t}$. Solving such optimization variants approximately, we may obtain a reconfiguration sequence comprising almost-satisfying truth assignments. In this study, we prove a series of gap-preserving reductions to give evidence that a host of reconfiguration problems are PSPACE-hard to approximate, under some plausible assumption. Our starting point is a new working hypothesis called the Reconfiguration Inapproximability Hypothesis (RIH), which asserts that a gap version of Maxmin CSP Reconfiguration is PSPACE-hard. This hypothesis may be thought of as a reconfiguration analogue of the PCP theorem. Our main result is PSPACE-hardness of approximating Maxmin $3$-SAT Reconfiguration of bounded occurrence under RIH. The crux of its proof is a gap-preserving reduction from Maxmin Binary CSP Reconfiguration to itself of bounded degree. Because a simple application of the degree reduction technique using expander graphs due to Papadimitriou and Yannakakis does not preserve the perfect completeness, we modify the alphabet as if each vertex could take a pair of values simultaneously. To accomplish the soundness requirement, we further apply an explicit family of near-Ramanujan graphs and the expander mixing lemma. As an application of the main result, we demonstrate that under RIH, optimization variants of popular reconfiguration problems are PSPACE-hard to approximate.

cs.DM↗

arXiv2023

A Critical Reexamination of Intra-List Distance and Dispersion

Diversification of recommendation results is a promising approach for coping with the uncertainty associated with users' information needs. Of particular importance in diversified recommendation is to define and optimize an appropriate diversity objective. In this study, we revisit the most popular diversity objective called intra-list distance (ILD), defined as the average pairwise distance between selected items, and a similar but lesser known objective called dispersion, which is the minimum pairwise distance. Owing to their simplicity and flexibility, ILD and dispersion have been used in a plethora of diversified recommendation research. Nevertheless, we do not actually know what kind of items are preferred by them. We present a critical reexamination of ILD and dispersion from theoretical and experimental perspectives. Our theoretical results reveal that these objectives have potential drawbacks: ILD may select duplicate items that are very close to each other, whereas dispersion may overlook distant item pairs. As a competitor to ILD and dispersion, we design a diversity objective called Gaussian ILD, which can interpolate between ILD and dispersion by tuning the bandwidth parameter. We verify our theoretical results by experimental results using real-world data and confirm the extreme behavior of ILD and dispersion in practice.

cs.IR↗